EXCHANGE 


THE  EFFECT  OF  TEMPERATURE  -ON  THE 

CHANGE  OF  RESISTANCE  OF  BISMUTH 

FILMS  IN  A  MAGNETIC  FIELD 


HY 


LEON  FRANCIS  CURTISS 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL 
OF  CORNELL  UNIVERSITY  FOR  THE  DEGREE  OF 

DOCTOR  OF  PHILOSOPHY 


lA 


Reprinted  from  PHYSICAL  REVIEW,  pp.  255-274,  Vol.  XVIII,  No.  4,  October,  1921 


Reprinted  from  the  PHYSICAL  RKVIRW.  N.S.,  Vol.  XVIII,  No.  4,  October,  1921, 


PHYSICAL   PROPERTIES   OF  THIN   METALLIC   FILMS.1 

III.     THE  EFFECT  OF  TEMPERATURE  ON  THE  CHANGE  OF  RESISTANCE 
OF  BISMUTH  FILMS  IN  A  MAGNETIC  FIELD. 

BY  L.  F.  CURTISS. 

SYNOPSIS. 

Ageing  of  sputtered  bismuth  films. — The  films  sputtered  on  glass  between  sputtered 
gold  terminals,  were  sealed  in  glass  tubes  and  kept  in  vacuo  at  210-220°  C.  for  a 
number  of  hours.  As  a  result  each  film  showed  a  gradual  decrease  of  resistance 
amounting  in  all  to  about  40  per  cent.  Eventually  the  films  became  so  thoroughly 
aged  that  temperature-resistance  measurements  in  vacuo  could  be  accurately 
reproduced  over  long  periods. 

Increase  of  resistance  of  bismuth  films  in  a  magnetic  field  for  temperatures  from 
—  190°  to  230°  C. — The  isothermal  curves  obtained  for  each  film  by  varying  the 
field  up  to  18,000  gauss,  have  the  same  form  for  all  temperatures,  differing  only  by 
constant  factors,  and  closely  resemble  the  corresponding  curves  for  bismuth  in 
bulk.  The  percentage  increase  of  resistance  is  not  proportional  to  the  square  of 
the  field.  It  is  greater  the  lower  the  temperature  and  the  lower  the  resistance,  that 
is,  the  thicker  the  film,  reaching  a  value  about  1/5  that  of  bismuth  for  the  thickest 
film  tested. 

Variation  of  resistance  of  bismuth  films  with  temperature,  —  190°  to  230°  C. — The 
curves  are  parabolic  in  form,  showing  a  minimum  around  150-200°  C.;  the  lower  the 
resistance  of  the  film,  the  lower  the  temperature  of  minimum  resistance. 

Electrically  heated  oil  bath. — //  is  suggested  that  bakelite  is  a  suitable  material 
for  protecting  the  nichrome  heater. 

THIS  work  continues  the  investigation  of  the  behavior  of  the  re- 
sistance of  bismuth  films  in  a  magnetic  field  described  in  the 
second2  paper  of  this  series.  A  study  of  the  change  of  resistance  of  these 
films  in  a  magnetic  field  at  various  constant  temperatures  from  near  the 
melting  point  of  bismuth  down  to  liquid  air  temperatures  has  here  been 
undertaken. 

1  Third  of  a  series  of  articles  on  this  subject  from  the  Physical  Laboratory  of  Cornell 
University.     This  series  of  articles  was  made  possible  by  a  grant  to  Prof.  F.  K.  Richtmyer 
from  the  Rumford  Fund. 

2  F.  K.  Richtmyer  and  L.  F.  Curtiss,  PHYS.  REV.,  15,  p.  465,  1920. 

255 


•  ••  ''*:     L- F-  CURTISS- 

For  this  purpose  thoroughly  aged  films  were  desirable,  since  only  with 
films  which  have  been  subjected  to  a  thorough  heat  treatment  can 
reproducible  results  be  expected,  as  is  evident  from  the  results  of  the 
previous  work  referred  to  above.  Since  the  oil  bath  had  not  been  entirely 
satisfactory  because  of  its  destructive  action  on  the  films,  it  was  thought 
advisable  to  try  some  other  means  of  protecting  the  films  from  the 
action  of  the  air  during  the  heating.  The  procedure  which  suggested 
itself  was  to  place  the  films  in  flat  glass  tubes  and  to  evacuate  the  tubes 
to  as  high  a  degree  as  possible  with  a  Langmuir  mercury  vapor  pump, 
at  the  same  time  heating  them  and  the  enclosed  films  to  near  the  melting 
point  of  bismuth.  This  heating  served  two  purposes.  It  gave  the  films 
a  preliminary  heat  treatment  and  it  also  helped  to  free  the  film  and 
tube  from  adsorbed  gases,  thus  affording  a  greater  protection  to  the  film 
during  subsequent  heatings.  ' 

The  films  were  prepared  in  much  the  same  way  as  for  the  previous 
work  (loc.  cit.}.  The  glass  slides  on  which  the  metal  was  deposited 
were  made  somewhat  narrower  for  convenience  in  inserting  them  into  the 
flat  glass  tubes.  The  actual  dimensions  of  the  bismuth  film  itself,  how- 
ever, were  kept  the  same  as  those  used  formerly,  i.e.,  10  by  3  mm.  The 
rotating  sector  was  dispensed  with  and  a  kenotron1  for  rectifying  the 
secondary  current  of  the  transformer  was  placed  in  series  with  the  dis- 
charge jar.  This  improvement  cut  out  the  reverse  current  and  eliminated 
its  heating  effect,  thus  rendering  the  rotating  sector  unnecessary  for 
the  preparation  of  films  for  the  present  purpose.  It  also  made  possible 
the  sputtering  of  much  thicker  films  than  had  previously  been  possible. 
For,  as  stated  in  the  preceding  paper,  after  sputtering  a  certain  length  of 
time  the  surface  of  the  bismuth  film  becomes  gray  and  powdery  and 
further  sputtering  has  little  effect  upon  the  resistance  of  the  film,  since 
the  particles  of  metal  which  come  down  seem  no  longer  to  adhere  to  the 
metal  already  deposited  firmly  enough  to  become  active  in  conducting 
the  current.  It  was  found  that,  this  condition  did  not  come  about  as 
soon  when  the  kenotron  was  used. 

The  successive  steps  in  the  manufacture  of  a  film  are  illustrated  in  the 
diagrams  in  Fig.  I,  which  are  drawn  to  scale.  First  the  glass  slide  was 
thoroughly  cleaned  chemically,  rinsed  with  distilled  water  and  dried. 
It  was  then  covered  across  the  middle  squarely  with  a  glass  slide  exactly 
i  cm.  wide  with  edges  ground  true  and  gold  terminals  were  deposited  on 
the  exposed  ends  by  cathodic  sputtering,  after  which  it  had  the  appear- 
ance indicated  in  Fig.  I,  a.  Then  a  shield  of  mica  with  a  slot  3  mm. 
wide  and  long  enough  to  overlap  the  gold  terminals  was  placed  on  this 
blank  and  a  bismuth  film  deposited,  likewise  by  cathodic  sputtering, 


NoL  4?VIH'J    PHYSICAL   PROPERTIES    OF    THIN    METALLIC   FILMS.  2^"/- 


along  the  center  of  the  slide  connecting  the  two  gold  terminals,  as  shown 
in  Fig.  i,  &.  A  piece  of  fine  bare  copper  wire  was  then  wrapped  tightly 
around  each  end  as  shown  in  Fig.  I,  c.  A  thin  layer  of  hot  paraffin  was 
spread  across  the  face  of  the  film,  near  the  ends  of  the  bismuth,  which 
prevented  the  copper  sulphate  solution,  used  in  plating  the  wires  in 
position,  from  creeping  up  on  to  the  bismuth.  This  was  later  dissolved 
off  with  xylol.  First  one  end,  then  the  other,  of  the  film  was  dipped 
into  the  plating  bath  and  a  thick  coating  of  copper  deposited  on  the  gold 
film  and  copper  wire,  the  projecting  wires  serving  as  leads  for  the  current 
in  each  case  so  that  it  did  not  pass  through  the  bismuth  film.  This 
plated  terminal  insured  positive  contact  with  the  film  at  all  temperatures 
and  proved  to  be  far  superior  to  the  clamps  which  had  been  used  before 
for  this  purpose.  The  film  at  this  stage  had  the  appearance  shown  in 
Fig.  i,  d.  Short  pieces  of  Cunife  wire  were  then  welded  onto  the  pro- 
jecting ends  of  the  copper  wires  for  sealing  through  the  glass  and  then 
longer  pieces  of  copper  wire  were  welded  onto  the  Cunife  to  serve  as 
external  leads  after  the  films  had  been  sealed  into  the  glass  tubes.  The 
tubes  were  prepared  from  flat  glass  tubing  by  sealing  a  short  piece  of 
glass  tubing  at  right  angles  near  one  end  for  attaching  to  the  pumps. 
The  film  with  its  lead  wires  was  then  sealed  in  and  the  tube  sealed  on  to 
the  pumps  and  evacuated  for  several  hours  at  about  210.°  C.  with  a 
Langmuir  pump,  after  which  it  was  sealed  off.  The  general  arrange- 
ment of  the  film  within  its  evacuated  tube  is  also  shown  in  Fig.  i.  The 


Fig.  1. 

film  was  now  further  aged  by  heating  for  four  hour  periods  to  about 
220°  in  an  oil  bath.  These  heatings  were  repeated  four  or  five  times 
for  each  film  after  which  it  had  become  relatively  stable  and  further 
heating  had  very  little  effect  upon  its  resistance  at  room  temperature. 

1  Kindly  loaned  by  Prof.  J.  S.  Shearer. 


T        r 

" 


rSKCOND 

[SERIES. 


It  is  interesting  to  note  that  all  films,  without  exception,  decreased  in 
resistance  as  a  result  of  this  heating.  This  is  quite  contrary  to  the 
effect  produced  by  heating  bismuth  films  in  air,  or  even  in  an  oil  bath, 
since  only  in  the  case  of  two  films  out  of  a  couple  of  dozen  did  such  an 
effect  occur  in  the  previous  work  (loc.  cit.}.  Thus  Film  V—  5  had  a 
resistance  of  36.7  ohms  at  room  temperature  after  it  had  been  sealed 
into  a  glass  tube  and  the  tube  exhausted.  After  it  had  been  subse- 
quently heated  for  four  hours  at  about  220°  its  resistance  at  room  tem- 
perature was  only  21.7  ohms,  thus  decreasing  about  41  per  cent,  in 
resistance  during  this  treatment.  Similarly  Film  V—  13  had  a  resistance 
after  being  sealed  into  a  tube  of  30.8  ohms  and  after  heating  eight  hours 
to  about  the  same  temperature  it  had  a  resistance  of  17.8  ohms,  or  had 
decreased  about  42  per  cent,  in  resistance.  Other  films  showed  com- 
paratively smaller  changes  during  this  aging  process  and  in  consequence 
were  less  stable,  and  showed  further  decreases  in  resistance  during  sub- 
sequent measurements  at  the  higher  temperatures.  Thus  the  resistance 
of  Film  V~9  was  10.9  ohms  after  having  been  sealed  into  a  tube  and 
after  heating  for  four  hours  its  resistance  was  7.4  ohms,  decreasing  about 
33  per  cent.;  similarly  Film  V-I4  had  a  resistance  of  100.0  ohms  after  it 
was  sealed  into  a  glass  tube  and  after  heating  eight  hours  its  resistance 
was  83.6  ohms,  decreasing  only  sixteen  per  cent.  Before  the  final  meas- 
urements on  this  film  had  been  taken,  however,  it  had  decreased  to  about 
55  ohms. 

For  measurements  in  the  field  at  room  temperature  and  above,  a  brass 
container  for  an  oil  bath  was  constructed.  It  consisted  of  two  brass 
tubes,  each  cut  away  on  one  side  and  joined  by  a  narrower  neck  so  as  to 
fit  in  between  the  pole-pieces  of  the  magnet.  A  step-bearing  was  fastened 
in  the  center  of  the  bottom  of  each  tube  in  which  a  vertical  shaft  carrying 
a  propeller  for  stirring  was  mounted.  These  shafts  were  provided  with 
pulleys  at  the  top  which  were  connected  by  means  of  idlers  with  an  end- 
less belt  which  also  passed  around  the  pulley  of  a  small  motor.  The 
shafts  were  so  driven  that  one  propeller  forced  the  oil  down  one  cylinder 
and  the  other  pulled  it  up  in  the  other  cylinder  so  that  a  continuous 
circulation  of  oil  was  produced.  Fig.  2  shows  a  plan  of  the  container 
and  illustrates  its  position  with  reference  to  the  pole-pieces  of  the  magnet. 
The  bath  was  about  12  cm.  deep  and  22  cm.  from  the  outside  of  one 
cylinder  to  the  outside  of  the  opposite  cylinder.  The  distance  between 
the  pole-pieces  was  one  centimeter.  The  bath  was  heated  by  a  resistance 
element  made  by  winding  nichrome  ribbon  on  a  sheet  of  mica.  It  was 
found  that  some  protection  for  the  ribbon  was  necessary  since  the  oil, 
although  it  was  a  good  grade  of  gas-engine  cylinder  oil,  carbonized  badly 


PHYSICAL   PROPERTIES   OF    THIN    METALLIC   FILMS. 


259 


at  the  higher  temperatures  and  adhered  to  the  ribbon,  thus  short- 
circuiting  adjoining  turns.  Bakelite  was  found  very  satisfactory  for 
this  purpose.  The  current  through  the  heating  element  could  be  con- 
trolled by  rheostats  so  that  the  temperature  could  be  brought  to  any 
desired  value  and  held  constant  for  considerable  intervals  of  time.  The 
temperatures  were  measured  with  a  copper-advance  thermo-couple  made 
and  calibrated  in  the  usual  way.  Its  e.m.f.  was  measured  by  a  Leeds 
and  Northrup  potentiometer. 


Fig.  2. 

Since  simultaneous  measurements  of  field  strength  and  resistance  of 
the  film  were  impracticable,  a  calibration  of  the  magnet  was  made  before 
the  temperature  bath  was  inserted  between  the  pole-pieces.  This  was 
done  by  means  of  a  bismuth  spiral,  calibrated  for  the  purpose  by  the 
Bureau  of  Standards.  Especial  precautions  were  taken  to  keep  the  spiral 
during  these  measurements  at  the  constant  temperature  at  which  it  had 
been  calibrated.  By  this  means  a  curve  between  the  current  through 
the  magnet  coils  and  the  strength  of  the  resulting  field  in  kilogauss  was 
obtained  which  was  used  in  determining  the  field  throughout  the  experi- 
ments at  room  temperature  and  above.  Control  experiments  showed 
that  this  method  would  give  results  which  could  be  depended  upon  to 
within  less  than  one  per  cent.,  which  was  deemed  adequate  for  the  present 
work.  The  current  for  the  magnet  was  supplied  by  a  set  of  twenty-six 
15-ampere  storage  cells  connected  in  series.  The  maximum  current 'used 
in  this  part  of  the  work  was  about  seven  amperes.  A  large  Weston 
Laboratory  Standard  millivoltmeter  and  shunt  were  used  in  measuring 
the  magnet  current  both  during  the  calibration  and  throughout  the 
subsequent  experiments. 

For  convenience,  all  the  measuring  instruments  and  controlling  rheo- 
stats were  mounted  on  a  table  so  that  they  were  all  under  the  control  of 
one  operator.  Thus  all  factors  could  be  varied  by  a  single  person 
without  shift  of  position  during  an  experiment.  This  also  made  possible 
a  simultaneous  determination  of  the  various  quantities,  eliminating 


260 


L.    F.    CURTISS. 


[SECOND 

[.SERIES. 


errors  due  to  variation  in  the  temperature  or  in  the  current  through  the 
magnet. 

In  making  the  measurements  the  procedure  was  as  follows:  The  film 
was  placed  in  its  position  in  the  oil  bath  and  the  rheostats  controlling 
the  current  through  the  heating  element  were  adjusted.  About  twenty 
minutes  were  necessary  for  the  temperature  to  become  steady.  As 
soon  as  the  potentiometer  readings  indicated  that  this  state  had  been 
reached,  measurements  of  the  resistance  of  the  film  were  made  at  various 
values  of  the  current  through  the  magnet  coils,  checking  the  zero-field 
resistance  of  the  film  and  the  potentiometer  reading  after  each  measure- 
ment. It  was  found  possible  in  all  cases  to  hold  the  temperature  steady 
enough  so  that  the  zero-field  resistance  of  the  film  did  not  vary  more  than 
o.i  per  cent,  during  a  series  of  measurements  at  a  given  temperature. 
The  results  of  the  measurements  can  best  be  presented  by  a  discussion 
of  the  curves  plotted  from  the  data  taken  with  typical  films.  A  set 
of  data  for  one  of  the  films,  V-5,  is  given  below  to  illustrate  the  magni- 
tude of  the  quantities  involved. 

FILM  V-5. 

Potentiometer  Reading,  o.ooioio;  Temperature,  23.5°;  Resistance  of  leads,  0.370  ohms. 


Magnet 
Current. 

Bridge 
Reading. 

Resistance 
of  Film. 

dr 

drlr 

H 

(Gauss). 

1.0 
0 

21.603 
21.509 

21.233 
21.139 

0.094 

0.0044 

2300 

2.0 
0 

21.862 
21.516 

21.492 
21.146 

0.346 

0.0164 

4725 

3.0 
0 

22.219 
21.502 

21.849 
21.132 

0.717 

0.0339 

7250 

4.0 
0 

22.682 
21.498 

22.312 
21.128 

1.184 

0.0561 

9700 

5.0 
0 

23.170 
21.492 

22.800 
21.122 

1.678 

0.0795 

11950 

6.0 
0 

23.660 
21.492 

23.290 
21.122 

2.168 

0.1028 

14125 

6.84 
0 

24.014 
21.493 

23.644 
21.123 

2.521 

0.1196 

15710 

Another  set  of  data  for  the  same  film  at  230°,  the  maximum  tempera- 
ture at  which  measurements  were  made  on  this  film,  is  given  below  also. 


PHYSICAL    PROPERTIES   OF    THIN    METALLIC   FILMS. 


26  1 


Temperature  variations  are  more  likely  to  occur  and  the  zero-field  re- 
sistance of  the  film  is  not  as  constant  as  in  the  set  taken  at  room  tempera- 
ture. However  the  variations  in  it  are  still  less  than  o.i  per  cent. 

Potentiometer  Reading,  0.011241;  Temperature,  229.3°. 


Magnet 
Current. 

Bridge 
Reading. 

Resistance 
of  Film. 

dr 

dr/r 

H 

0 

20.957 

20.587 

1.0 

20.943                20.573 

0 

20.930                20.560 

0.013 

0.0005 

2300 

2.0 

20.965                20.595 

0 

20.938                20.568 

0.027 

0.0013 

4725 

3.0 

21.001 

20.631 

0 

20.930 

20.560 

0.071 

0.0034 

7250 

4.0 

21.039                20.669 

0 

20.930 

20.560 

0.109 

0.0053 

9700 

5.0 

21.086                20.716 

"' 

0 

20.925                20.555 

0.161 

0.0078 

11950 

6.0 

21.141 

20.771 

0 

20.923 

20.553 

0.218 

0.0106 

14125 

6.8 

21.186 

20.816 

0 

20.921 

20.551 

0.265 

0.0129 

15650 

For  measurements  at  low  temperatures  the  oil  bath  was  removed  from 
between  the  pole-pieces  of  the  magnet,  and,  to  make  possible  better 
heat  insulation,  the  pole-pieces  were  separated  to  a  distance  of  1.8  cm. 
The  exposed  parts  of  the  magnet  in  between  the  coils  were  covered  with 
a  thick  layer  of  heat  insulation,  a  thinner  layer  also  covering  the  faces 
of  the  pole-pieces.  A  cardboard  container  for  the  refrigerant  was 
lowered  into  the  rectangular  compartment  thus  formed.  A  vertical 
section  is  shown  in  Fig.  3  which  will  give  an  idea  of  the  arrangement. 

Since  the  pole-pieces  of  the  magnet  had  been  separated  to  a  greater 
distance  it  was  necessary  to  increase  the  current  through  the  coils, 
beyond  that  which  was  used  during  the  experiments  at  the  higher  tem- 
peratures, in  order  to  cover  the  same  range  of  field  strengths.  The 
magnet  was  accordingly  connected  to  the  no-volt  direct  current  supply 
of  the  laboratory  through  suitable  rheostats.  This  arrangement  was 
not  as  satisfactory  as  the  storage  battery  had  been  since  the  fluctuations 


262 


L.    F.    CURTISS. 


[SECOND 

LSERIES. 


Fig.  3. 


in  the  line  voltage  caused  small  variations  in  the  magnet  current.  How- 
ever, by  exercising  extreme  care,  errors  from  this  source  could  be  reduced 
to  a  negligible  amount.  The  maximum  current  used  was  about  18 
amperes,  giving  a  field  of  about  18,000  gauss.  The  magnet  was  recali- 
brated, a  ballistic  galvanometer,  a  standard  of  mutual  in- 
ductance, and  a  snatch  coil  being  used  for  this  purpose, 
since  an  accident  to  the  bismuth  spiral  had  ruined  it. 

The  films  were  removed  from  their  protecting  glass  tubes 
for  the  measurements  at  low  temperatures,  as  they  have 
very  slight  tendency  to  oxidize  at  room  temperature  and 
below,    and  a  considerable  saving  of   space  between  the 
pole-pieces  was  thereby  accomplished .     They  were  mounted 
on  a  fiber   support  by  means  of   which  they  were   accu- 
rately centered  between  the  pole-pieces.      One  junction  of 
a    thermo-couple    for   measuring    temperatures    was    also 
mounted  on  the  fiber  strip  so  that  it  was  close  to  the  film. 
Great  difficulty,  due  to  poor   heat   insulation   and   the 
conductivity  of  the  large  pole-pieces,  was   experienced   in 
maintaining  constant  temperatures  for  any  considerable 
period  of  time  unless  the  films  were  actually  immersed  in 
the    refrigerant.      Consequently    measurements    in    the  field  were  only 
attempted  when  the  films  were  immersed  in  either  a  mixture  of  carbon 
dioxide  snow  and  ether  or  in  liquid  air. 

The  results  of  the  investigation  can  be  considered  under  four  heads, 
viz.,  (i)  effect  of  magnetic  field  on  the  resistance  of  the  films  at  various 
temperatures;  (2)  the  dependence  of  the  values  of  the  percentage 
increase  of  resistance  upon  the  thickness  of  the  film;  (3)  evidences  of 
aging  of  the  films;  (4)  relation  between  the  temperature  of  the  film  and 
its  resistance. 

Observations  were  made  on  the  behavior  of  a  large  number  of  films 
varying  in  resistance  from  7  ohms  to  70  ohms.  No  attempts  were  made 
to  measure  the  thickness  of  the  films.  Since  all  of  the  films  had  the 
same  length  and  breadth,  the  resistance  can  be  taken  as  a  rough  indication 
of  the  thickness.  Film  V-io  has  been  selected  as  an  example  for  a 
discussion  of  the  effect  of  temperature  upon  the  percentage  increase  of 
resistance  of  the  films  in  a  magnetic  field.  At  20.5°  its  resistance  was 
10.54  ohms,  hence  it  was  one  of  the  thicker  films  studied.  The  results 
of  the  measurements  on  this  film  at  various  temperatures  are  shown 
graphically  in  Fig.  4.  The  percentage  increase  of  resistance  has  been 
plotted  against  the  field  strength  in  kilogauss.  The  various  curves  have 
been  labelled  and  were  taken  at  the  following  temperatures: 


PHYSICAL   PROPERTIES   OF    THIN    METALLIC   FILMS. 


263 


I. 

II 

ill 


20.5C 

57.2C 
109.0C 


IV 147.5' 

V 195° 

VI..          ..227° 


VII -    80° 

VIII -  190° 

A..  19.5< 


As  the  temperature  decreases  the  effect  of  the  field  becomes  more 
strongly  marked,  especially  at  the  low  temperatures.  For  the  weaker 
fields  there  is  a  decided  curvature  in  the  lines  which  gradually  smooth 


z 


<z 


These  curves  represent  the  values  of  drfr  at  various  temperatures  and  values  of  the  field 

for  Film  V-io. 

out  into  practically  straight  lines.  It  is  in  this  lower  region  that  the 
"square  law,"  proposed  by  Sir  J.  J.  Thomson,1  holds.  As  a  check  on 
the  reproducibility  of  the  results  the  data  for  Curve  /  were  retaken 
immediately  after  taking  the  data  for  Curve  //.  The  result  is  shown 
by  the  crosses  (x)  which  practically  coincide  with  the  circles  used  to 
represent  the  initial  data.  Curve  A  was  taken  after  Curve  VI  and  also 
after  a  subsequent  temperature-resistance  run  had  been  made  with  the 
film.  The  significance  of  the  location  of  this  curve  will  be  discussed 
later  in  connection  with  evidences  of  aging  in  these  films.  The  curves 
labelled  (/),  (//),  and  (III)  were  obtained  by  multiplying  the  ordinates 

1  J.  J.  Thomson,  Rapports  presentes  au  Congres  International  de  Physique,  1900. 


264 


L.    F.    CURTISS. 


[SECOND 

[SERIES. 


of  the  corresponding  curves  below  by  four.  This  has  been  done  in  order 
that  it  may  be  made  plain  that  the  form  of  the  curves  is  the  same  through- 
out, so  that  the  only  effect  of  the  change  of  temperature  is  to  multiply 
the  ordinates  by  a  constant  amount  for  any  particular  film.  This  is  a 
rather  significant  and  unexpected  result.  If  we  express  the  equation  of 
the  family  of  curves  in  terms  of  dr/r  and  some  function  of  the  field  we 
may  do  so  as  follows: 

dr/r  =  kf(H) 

where  k  is  a  constant  which  depends  on  the  temperature. 

In  Fig.  5  the  effect  of  temperature  is  shown  more  directly  for  a  similar 
film,  V~9,  where  dr/r  is  plotted  against  the  temperature  for  several 


H-lb 


70 


'60 


H-IZ 


\ 


\ 


\ 


\ 


\ 


lempor«/ur« 

Fig.  5. 

These  curves,  representing  results  obtained  with  Film  V-p,  shows  directly  the  effect  of 
temperature  on  the  values  of  dr/r  at  a  number  of  constant  field  strengths. 

constant  values  of  the  field.  Here  again  we  see  that  as  the  temperature 
decreases  the  field  produces  correspondingly  greater  values  of  the  increase 
of  resistance.  As  in  bismuth  in  bulk,1  these  curves  indicate  that  the 
increase  of  resistance  would  vanish,  or  become  very  small,  at  least,  at 

1  Drude  and  Nernst,  Gott.  Nachrichten,  No.  14,  p.  471,  1890. 


NoL'*VI11']    PHYSICAL    PROPERTIES    OF    THIN    METALLIC   FILMS.  265 

the  melting  point  of  the  metal.  In  form  the  curves  are  very  similar  to 
the  curves  representing  the  same  quantities  for  bismuth  in  bulk.  In 
fact,  all  measurements  made  on  these  films  in  the  magnetic  field  support 
the  statement  that  they  differ  mainly  from  solid  bismuth  in  the  magnitude 
of  the  changes  produced  by  the  field. 

In  order  to  give  a  basis  for  comparison  of  this  series  of  films  with  those 
described  in  the  previous  paper  (loc.  cit.),  in  which  the  results  were  repre- 
sented by  plotting  the  percentage  increase  of  resistance  against  the 
square  of  the  field,  a  similar  set  of  curves  has  been  prepared  for  Film 
¥-9.  Since  this  film  was  of  somewhat  lower  resistance  than  V-io, 
Fig.  4,  it  yielded  larger  values  of  dr/r  under  similar  conditions.  The 
result  is  shown  in  Fig.  6.  It  is  quite  evident  that  the  values  of  dr/r  are 
not  directly  proportional  to  the  square  of  the  field  for  these  films  as  they 
seemed  to  be  for  those  studied  in  the  previous  work.  However,  at  the 
higher  temperatures,  where  the  values  of  dr/r  are  small,  there  seems  to 
be  an  approach  to  such  a  proportionality  for  these  films.  This  item  is 
also  quite  in  agreement  with  all  previous  work  on  this  subject  which  has 


Data  for  Film  V-Q  showing  that  the  values  of  dr/r  are  not  proportional  to  the  square  of  the 

field. 

led  to  the  conclusion  that  only  where  the  effect  of  the  field  is  small  does 
the  square  law  obtain,1  and  it  seems  to  matter  little  as  to  what  the  cause 
of  the  smallness  is,  whether  the  nature  of  the  substance  or  its  condition. 
However,  the  result  of  this  work  tends  to  show  that  if  the  values  of  dr/r 
have  been  diminished  by  raising  the  temperature  of  a  substance  for  which 
the  square  law  did  not  hold  at  lower  temperatures,  it  will  also  not  hold 
at  the  higher  temperatures.  On  the  other  hand  there  may  be  a  limit 
above  which  the  equation  proposed  in  connection  with  the  results  shown 
in  Fig.  4  does  not  hold,  although  at  present  there  is  no  evidence  of  it 
within  the  range  of  temperatures  here  covered.  It  would  be  interesting 

1  S.  C.  Laws,  Phil.  Mag.,  19,  p.  685,  1910. 


266 


L.    F.    CURTISS. 


[SECOND 

[SERIES. 


to  study  the  behavior  of  bismuth  in  bulk  in  weak  fields,  up  to  3  kilo- 
gauss,  to  determine  whether  this  square  law  holds  when  the  values  of  dr/r 
are  small  as  a  result  of  the  low  values  of  the  field  strength  used  for  a 
substance  which  does  not  obey  the  law  in  stronger  fields.  Although  the 
tendency  has  been  to  assume  that  it  did  hold  in  this  region,  as  far  as  the 
writer  is  aware,  special  attention  has  never  been  given  to  measurements 
in  very  weak  fields. 

For  a  discussion  of  the  dependence  of  the  values  of  dr/r  upon  the  thick- 
ness of  the  film,  which  can  only  be  considered  here  in  a  qualitative  way, 
the  following  series  of  films  has  been  chosen : 

Film  V-14,  —  Resistance  54.88  ohms  at  24.5°. 
Film  V-13,  —  Resistance  17.48  ohms  at  21.0°. 
Film  V-10,  —  Resistance  10.54  ohms  at  20.5°. 
Film  V-  9,  —  Resistance  7.07  ohms  at  20.5°. 

The  corresponding  data  for  these  various  films  have  been  plotted  in 
Fig.  7.  Each  curve  was  taken  at  the  temperature  given  above  in  con- 
nection with  the  zero-field  resistance  of  the  film.  These  curves  show 


H 

Fig.  7. 
Curves  showing  the  results  for  films  of  various  thicknesses  at  room  temperature. 

that  the  films  of  lower  resistance  have  a  larger  value  of  dr/r  under  similar 
conditions.  This  is  rather  to  be  expected  since  the  thicker  the  film  the 
closer  the  approach  to  solid  bismuth.  To  show  further  that  no  essential 
change  in  the  form  of  the  curve  occurs  as  the  thickness  of  the  film  in- 


PHYSICAL   PROPERTIES   OF    THIN   METALLIC    FILMS. 


267 


creases,  the  ordinates  for  V-I4  have  been  multiplied  by  three  and  re- 
plotted  as  indicated  by  the  dotted  curve  which  runs  quite  parallel  to  the 
neighboring  curve  for  V-io.  In  Fig.  8  the  similar  results  obtained  for 
V-9,  V-io,  and  V-I4  at  the  temperature  of  liquid  air  are  shown.  Here 
the  difference  between  V— 9  and  V— 10  is  much  greater,  indicating  that 
the  thicker  films  have  a  comparatively  greater  value  of  dr/r  at  the  lower 
temperatures,  a  further  evidence  that  in  them  the  conditions  are  more 
nearly  approaching  those  in  solid  bismuth. 


100 


70 


(,0 


H 

Fig.  8. 

Showing  the  effect  of  thickness  of  the  film  upon  the  values  of  drfr  at  the  temperature  of 
liquid  air. 

A  discussion  of  the  evidences  of  aging  in  these  films  and  also  of  the 
form  of  the  temperature-resistance  curves  may  well  be  taken  up  together, 
since  they  are  closely  related.  The  temperature-resistance  curves  for 
Films  V-I4,  V-I3,  ¥-5,  and  V-io  are  shown  in  Figs.  9,  10,  n,  and  12, 
respectively.  In  Fig.  9  we  have  a  typical  curve  for  a  film  of  higher 
resistance.  It  is  to  be  noted  that  the  first  cooling  curve  is  exactly 
retraced  by  the  second  heating  curve  and  the  second  cooling  curve,  where- 
as the  first  heating  curve  lies  somewhat  above  these  three.  The  ex- 
planation for  this  behavior  is  evident  when  attention  is  called  to  the  fact 
that,  as  shown  by  the  curves,  care  was  taken  in  making  the  second  heating 
not  to  exceed  the  previous  maximum  temperature  for  the  first  heating. 


268 


L.    F.    CURTISS. 


SECOND 
SERIES. 


Hence  no  further  aging  occurred  during  the  second  heating  and  the 
resistance  remained  unchanged.  This  plainly  shows  that  this  film  had 
not  had  its  aging  process  carried  to  the  limit  before  the  temperature- 


art- 

53 
52 
Si 
50 
tl 

i 

¥6 
*5 

*3 

< 

q 

Film  V-l* 

0-F,ril  Hettint          9-  Second  Httlns 
-$~    *   Cooling           &-    ••     Cocliiy 

\ 

i 

\ 

\  \ 

\ 

\ 

\ 

A 

^  ^ 

, 

\ 

\ 

I 

\ 

V 

\ 

. 

\ 

\ 

A 

\ 

\ 

^v 

^ 

s^ 

A\ 

x. 

\ 

^>>^ 

fi«^ 

^7 

^ 

y       2J*      *>•      w      xw     /EJ*     /so-     ny     zoo"    & 

Temperature 

Fig.  9. 

resistance  measurements  here  shown  were  undertaken,  and  that  in  making 
the  first  heating  the  previous  maximum  temperature  to  which  the  film 
had  been  heated  was  exceeded  with  a  resultant  decrease  in  resistance 


• 

Film     V-/3 

o  -  First  Htulina      &  -  Second  CW>« 
>-    «'  Ceofinj      0  -1ff4gHgy 
—  Second  /fc*rms  +-  "     c«<"« 

i 

\ 

\ 

\ 

I 

\ 

's 

\ 

9 

\ 

\ 

\ 

A\ 

^ 

^ 

i° 

,  ,Tcmi 

>e  r  a  fj 

/re 

^r- 

i.  10. 


VOL.  XVIII. 

No.  4 


]    PHYSICAL    PROPERTIES    OF    THIN    METALLIC   FILMS.  269 


of  the  film.  One  would  expect  then  that  this  would  show  itself  in  the 
behavior  of  the  film  in  the  magnetic  field.  Data  taken  in  the  magnetic 
field  before  and  after  these  temperature-resistance  measurements  yielded 


• 
* 

Film    V-5 

0  -  Fir»T  H  «  «ti  nj                •  -  S  ecortd  C.o/my 
•^-Second    '•                o-TA.rd  Hertinj 
A-rThird  Cooling 

20.0 
195 

\ 

/ 

I          \ 

1 

\ 

/ 

110 

\ 
\ 

/ 

. 

"emperalure 

Fig.  11. 

the  expected  result.  Since  too  many  figures  would  be  required  to  show 
all  the  results  in  detail,  an  idea  of  the  relative  magnitude  of  this  change 
produced  in  the  values  of  dr/r  may  be  obtained  by  reference  to  Fig.  4, 


IDA 


9.JS 


Y 

v 


Film 

0-finT  Heating 

•0-    "    Cooling 


V-/o 

•  -  Second He.f,»f 
A-     "      Cooling 


Temperature 


Fig.  12. 
The  above  figures  show  typical  temperature-resistance  curves  for  films  of  different  thickness. 


2  7°  L-    F-    CURTISS. 

where  the  similar  results  for  Film  V-io  are  represented.  The  curves 
labelled  /  and  A  show  the  behavior  of  this  film  when  treated  in  a  like 
manner.  Curve  /  was  taken  before  the  temperature-resistance  run  and 
Curve  A  afterwards  at  the  same  temperature.  The  result  of  the  aging 
was,  as  shown,  to  increase  the  values  of  dr/r.  A  further  point  of  interest 
in  Fig.  9  is  the  suggestion  of  a  minimum  value  of  the  resistance  at  about 
210°.  This  minimum  shows  much  more  clearly  in  the  curve  for  Film 
V— 13  in  Fig.  10.  It  occurs,  moreover,  at  a  lower  temperature,  in  the 
neighborhood  of  170°.  In  this  connection  it  is  to  be  noted  that  ¥-13 
has  a  considerably  lower  resistance  than  the  preceding  film.  Further- 
more the  preliminary  heat  treatment  was  carried  out  much  more  thor- 
oughly, the  results  of  which  are  strikingly  shown  by  the  reproducibility 
of  the  data.  The  observed  points  are  here  indicated  by  various  symbols 
for  three  heatings  and  three  coolings,  taken  over  a  period  of  several  days, 
and  yet  a  single  curve  represents  all  fairly  well;  only  the  very  slightest 
traces  of  aging  are  to  be  detected.  Likewise  it  was  found  possible  to 
reproduce  the  measurements  in  the  magnetic  field  with  similar  accuracy 
for  this  film.  These  results  are  quite  contrary  to  any  of  the  author's 
previous  experiences  with  sputtered  films.  In  fact,  it  had  always  been 
found  impossible  to  so  age  a  film  that  its  resistance  would  remain  con- 
stant for  more  than  a  few  hours  at  room  temperature,  while  exposed  to 
the  air,  and  reproducible  measurements  at  higher  temperatures  were 
out  of  the  question.  To  show  more  completely  the  form  of  the  tempera- 
ture-resistance curve  the  data  for  Film  V~5  are  shown  in  Fig.  1 1 .  Here 
both  branches  of  the  curve,  which  is  perfectly  symmetrical  and  in  form 
approaches  that  of  a  parabola,  are  well  defined.  This  film  also  has  been 
thoroughly  aged  and  the  minimum  resistance  has  shifted  to  a  still  lower 
temperature.  An  attempt  to  fit  a  parabolic  equation  to  this  curve  has 
been  made.  Although  the  deviations  are  slight,  they  seem  to  be  some- 
what greater  than  possible  experimental  errors.  All  previous  films  of 
bismuth  which  have  been  studied  by  the  author,  or  by  others,  so  far  as 
a  search  of  the  literature  has  revealed,  have  without  exception  had 
negative  temperature  coefficients  of  resistance.  We  have  here,  how- 
ever, an  example  where  the  coefficient,  initially  negative  at  room 
temperature,  actually  reverses  its  sign  as  the  film  is  heated  and  be- 
comes positive.  The  maximum  value  of  the  positive  coefficient  which 
has  been  obtained  is  far  less  than  that  for  bismuth  in  bulk,  roughly  of 
one  quarter  the  magnitude.  A  further  example  of  this  form  of  curve  is 
shown  in  Fig.  12,  representing  the  results  obtained  with  Film  V-io. 
This  is  another  example  of  a  film  that  has  been  only  partially  aged, 
hence  there  was  a  big  decrease  in  resistance  as  the  film  was  heated  for 


PHYSICAL   PROPERTIES   OF    THIN   METALLIC   FILMS. 


2JI 


the  first  time.  The  effect  of  the  second  heating,  as  was  to  be  expected, 
was  considerably  less,  although  it  was  carried  out  to  a  slightly  higher 
temperature.  The  symmetry  of  the  curves  is  considerably  distorted 
by  this  aging  effect  which  takes  place  at  the  higher  temperatures.  It 
is  to  be  noted  that  the  points  representing  the  second  heating  lie  closely 
on  the  curve  for  the  first  cooling,  until  the  higher  temperatures  are 
reached,  showing  that  the  aging  occurs  chiefly  at  temperatures  above  200°. 


\ 

nim  v-/t. 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

s 

^ 

r^~ 

Fig.  13. 
Showing  the  complete  temperature  resistance-curve  for  Film  V-io. 

In  Fig.  13  the  complete  temperature-resistance  curve  for  Film  V— 9 
is  represented.  The  part  from  room  temperature  to  230°  was  taken 
some  months  before  the  part  at  low  temperatures.  This  fact,  together 
with  the  effect  of  increased  pressure  to  which  the  film  was  subjected  when 
air  was  admitted  to  it,  accounts  for  the  jog  in  the  curve  at  o°.  If  the 
part  taken  at  the  higher  temperatures  were  raised  throughout  by  a 
constant  amount,  equal  to  the  difference  of  ordinates  at  o°,  the  two 
parts  would  then  form  a  smooth  curve  which  agrees  in  form  with  those 
taken  for  other  films  throughout  this  range  of  temperatures.  Hence 
there  seems  to  be  no  evidence  of  any  peculiarities  in  the  low  temperature 
part  of  the  temperature-resistance  curves  for  these  films. 

To  show  what  happens  to  one  of  these  films  when  it  is  heated  in 
contact  with  the  air,  a  temperature-resistance  run  for  Film  V-8  is  shown 
in  Fig.  14.  This  film  was  prepared  in  the  usual  way  and  during  the  first 
heating  and  cooling  behaved  much  the  same  as  had  all  previous  films 
which  were  thoroughly  aged,  the  two  sets  of  observations  lying  along  the 


272 


L.    F.    CURTISS. 


SECOND 

SERIES. 


same  curve.  However,  soon  after  the  beginning  of  the  second  heating, 
the  resistance  began  to  increase  rapidly.  After  cooling  down  it  had  a 
considerably  higher  resistance  than  before  at  room  temperature.  This 
anomalous  behavior  was  hard  to  explain  until  the  film  was  taken  out  of 
the  bath  and  examined.  It  was  then  discovered  that  a  yellowish  coating 
of  oxide  had  form  on  the  surface,  indicating  that  the  glass  tube  had  given 


29 


\ 


V 


Film    V-« 

O-fiv»T  Coolint  •- Second  He* ling 


TemperaTure 


Fig.  14. 

This  figure  shows  the  temperature-resistance  curve  obtained  for  Film  V-8,  which  was  attacked 
by  the  air  as  a  result  of  a  break  in  the  protecting  tube. 

way  at  some  point,  admitting  air.  On  further  examination  this  proved 
to  be  the  case.  There  seems  to  be  an  additional  effect  of  the  air  on  the 
form  of  this  curve  beyond  that  produced  by  oxidation  alone,  however. 
The  difference  in  ordinates  at  the  maximum  temperature  is  considerably 
greater  than  at  room  temperature,  hence  the  increase  of  resistance  at  the 
higher  temperature  is  not  all  permanent,  as  it  would  be  if  it  were  due 
solely  to  oxidation.  This  additional  effect  may  well  be  caused  by  the 
pressure,  although  this  point  was  not  specially  investigated. 

The  foregoing  covers  the  experimental  results  of  this  investigation. 
As  far  as  the  magnetic  measurements  are  concerned  little  more  can  be 
said  beyond  the  mere  statement  that  these  films  approach  the  behavior 
of  bismuth  in  bulk,  the  approach  being  nearer  the  thicker  the  film.  Any 
theoretical  discussion  of  these  results  and  interpretation  in  terms  of  the 
electron  theory  would  necessarily  follow  the  same  general  lines  as  those 
for  bismuth  in  bulk.  Too  little  is  known  at  present  with  any  degree  of 
certainty  about  the  nature  of  electrical  conduction  in  metals  to  enable 
very  much  progress  to  be  made  in  this  direction  beyond  what  has  already 
been  accomplished  by  Thomson  and  others.  This  is  very  clear  when 


PHYSICAL   PROPERTIES    OF    THIN    METALLIC   FILMS.  2 73 

attention  is  called  to  the  fact  that  the  most  successful  theories  so  far 
advanced,1  either  agree  with  the  experimental  data  only  for  very  limited 
ranges  of  the  field  strength,  or  require  properties  which  bismuth  does 
not  possess,  e.g.,  magnetostriction. 

It  is  also  difficult  to  explain  successfully  the  form  of  the  temperature- 
resistance  curves  of  these  films.  One  explanation  which  might  be 
offered  for  the  reversal  of  the  sign  of  the  temperature  coefficient  and  the 
consequent  minimum  resistance,  the  location  of  which  varies  from  film 
to  film,  and  is,  in  general,  at  a  lower  temperature  the  lower  the  resistance 
of  the  film,  is  as  follows:  It  is  based  on  the  fact  that  the  metal  particles 
have  a  larger  coefficient  of  thermal  expansion  than  the  glass.  Hence 
as  the  film  rises  in  temperature  they  expand  more  rapidly  and  bring 
more  particles  into  contact,  reducing  the  negative  temperature  coef- 
ficient of  resistance,  and  finally,  if  the  film  is  thick  enough,  the  particles 
are  crowded  close  enough  together  and  at  a  rate  fast  enough  to  reduce 
this  coefficient  to  zero,  then  finally  to  reverse  its  sign.  Then  the  metallic 
film  begins  to  behave  somewhat  like  the  metal  in  bulk,  but  is  prevented 
from  attaining  a  positive  coefficient  as  large  as  that  for  solid  bismuth 
by  the  fact  that  the  glass  also  continues  to  expand,  thus  preventing  the 
compacting  process  from  going  far  enough  to  establish  contact  between 
all  the  possible  particles.  The  study  of  this  phase  of  the  subject  is  limited 
by  the  comparatively  low  melting  point  of  bismuth  (about  260°).  This 
explanation  is  far  from  satisfactory,  however,  since  on  the  basis  of  it  a 
platinum  film  sputtered  on  glass  should  have  practically  a  zero  tempera- 
ture coefficient,  which  is  contrary  to  the  facts  as  reported  by  other 
observers.  But  then  there  must  be  taken  into  account  also  the  effect 
of  temperature  on  the  conductivity  of  the  metallic  particles  themselves. 
Hence  we  have  at  least  two  influences  which  must  be  considered  simul- 
taneously. The  first  is  that  due  to  the  difference  in  the  thermal  coef- 
ficients of  expansion  which  should  cause  an  increase  or  decrease  in  the 
number  of  possible  paths  for  electrons  from  particle  to  particle,  according 
as  the  film  is  heated  or  cooled.  The  second  is  that  which  results  from 
the  effect  of  temperature  upon  the  motions  of  the  electrons  within  the 
particles,  and  also  its  effect  upon  the  ease  with  which  an  electron  may 
detach  itself  from  one  particle  and  move  on  to  the  next.  This  view  of 
the  structure  of  the  films  is  strengthened  by  the  fact  that  x-ray  studies2 
of  the  films  indicated  that  they  were  composed  of  small  crystals  of  metal, 
with  random  orientation,  which  have  been  detached  from  the  cathode 
and  deposited  on  the  glass  during  sputtering.  This  view  is  in  contrast 

1  E.  P.  Adams,  PHYS.  REV.,  24,  p.  248,  1907. 

2  H.  Kahler,  PHYS.  REV.,  17,  p.  230,  1921. 


74  *-  F-  CURTISS. 

rith  the  evaporation  theory  which  holds  that  the  metal  of  the  cathode 

>  vaporized  and  then  condenses  on  the  glass,  in  which  case  a  film  of 
ntirely  different  structure  from  that  of  the  cathode  metal  might  result, 
lowever,  this  point  is  not  settled. 

For  further  comparison  of  the  results  here  given  with  those  obtained 
3r  bismuth  in  bulk,  a  reference  to  an  investigation  by  Dr.  F.  C.  Blake1 

>  included.     His  work,  published  in  1909,  covers  practically  the  same 
ange  for  the  solid  metal. 

SUMMARY. 

The  preceding  results  may  be  summarized  as  follows : 

1.  By  protecting  sputtered  bismuth  films  in  a  vacuum  and  heating 
hem  to  temperatures  near  the  melting  point  of  bismuth  it  is  possible  to 
evelop  the  property  of  an  increase  of  resistance  in  a  magnetic  field  to 
bout  one  fifth  that  possessed  by  bismuth  in  bulk. 

2.  The  higher  the  temperature  of  the  film  the  smaller  the  value  of  the 
•ercentage  increase  of  resistance  for  a  given  field. 

3.  The  form  of  the  curve  between  dr/r  and  field  strength  is  independent 
f  the  temperature  of  these  films,  i.e.,  dr/r  =  kf(H). 

4.  The   temperature-resistance  curves   for   these   films  are  parabolic 
ti  form,  and  the  minimum  resistance  is  at  a  lower  temperature  the  thicker 
he  film. 

5.  If  these  films  have  been  subjected  to  a  very  thorough  heat  treatment 
he   temperature-resistance   curve   is   fixed   and   definite.     Under  these 
onditions  reproducible  data  are  easily  obtained  in  the  magnetic  field. 

6.  If  the  film  is  only  partially  aged  it  decreases  in  resistance  with  con- 
inued  heating  and  exhibits  correspondingly  greater  values  of  dr/r  in  the 
nagnetic  field  as  a  result  of  the  heating. 

In  conclusion  I  wish  to  thank  Professors  Ernest  Merritt  and  F.  K. 
lichtmyer,  under  whose  direction  this  work  was  done,  and  all  others, 
yho,  by  advice  or  suggestions,  have  helped  the  progress  of  this  investi- 
gation. 

PHYSICAL  LABORATORY, 
CORNELL  UNIVERSITY. 

1  F.  C.  Blake,  Ann.  d.  Phys.,  28,  p.  449,  1909. 


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